{"paper":{"title":"The 3x3 lemma in the ${\\Sigma}$-Maltsev and ${\\Sigma}$-protomodular settings. Applications to monoids and quandles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Andrea Montoli, Dominique Bourn","submitted_at":"2018-01-27T15:38:13Z","abstract_excerpt":"We investigate what is remaining of the 3x3 lemma and of the denormalized 3x3 lemma, respectively valid in a pointed protomodular and in a Maltsev category, in the context of partial pointed protomodular and partial Maltsev categories, relatively to a class ${\\Sigma}$ of points. The results apply, among other structures, to monoids, semirings and quandles"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09104","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}